The deaths raise to 19 the number of militants killed since the attack near the North Sinai provincial capital of al-Arish early on Wednesday, which Islamic State claimed responsibility for.
The Interior Ministry said in a statement that security forces have tracked down militants who escaped after that to an abandoned house in Masaeed neighborhood in al-Arish.
"While they were being surrounded, they opened fire extensively towards the forces. They were engaged resulting in the death of 14 terrorist elements," the statement said.
It said 14 automatic weapons, three explosives devices and two suicide belts were found in their procession.
The statement did not say if any members of the security forces had been hurt during the gunfight.
A Reuters investigation in April found that Egyptian security forces had shot dead hundreds of suspected militants in what the Interior Ministry said were gun battles but which bereaved families said were extrajudicial executions.
A Reuters analysis of the ministry statements showed that deadly shootouts often followed an attack by militants.
Egypt denies any abuses and says its security forces operate within the country's legal framework.